Algorithms for Worst-Case Design and Applications to Risk Management

By Berç Rustem; Melendres Howe | Go to book overview

Chapter 9
Minimax and asset allocation problems

In this chapter, we consider potential uses of minimax in the context of portfolio asset allocation, with specific illustrations for bond portfolios. We demonstrate that the issue of mis-forecasting can be appropriately addressed within the minimax framework. An asset allocation based on minimax has robustness properties that cushion the performance of the portfolio against the occurrence of predefined worst-case scenarios. There is a guaranteed performance which improves when the worst-case scenario fails to materialize. A number of minimax asset allocation techniques are discussed, all applicable to stocks, bonds or currencies. These are considered in the context of meanvariance optimization and benchmark tracking. Additionally, a minimax formulation for a multistage asset allocation problem is presented. Lastly, the complementary use of both minimax and options for portfolio management is explored.


1 INTRODUCTION

In this chapter, we address the issue of asset allocation and present allocation strategies based on minimax that enable the investor to better assess the potential performance of a chosen portfolio. We initially consider two standard investment tools: the mean-variance and the benchmark-tracking approaches to portfolio selection. The extensions of these strategies to a minimax framework are explored with illustrations on how an investor can benefit from these extensions. Minimax index tracking is considered, showing how standard tracking techniques can be adapted to form robust trackers. A multistage framework for minimax portfolio selection is presented for portfolio rebalancing. Finally, the simultaneous use of minimax and options is studied in a complementary manner that allows a fund manager to benefit from lower insurance premia.

Starting with the work of Markowitz (1952) on portfolio selection, considerable work has been devoted to the issue of asset allocation. Markowitz proposed the idea that a sensible investing strategy does not look solely at return-maximization, but also at the interplay between return-maximization and risk-minimization, and the trade-off between these two. Hence, a balance

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Algorithms for Worst-Case Design and Applications to Risk Management
Table of contents

Table of contents

  • Title Page *
  • Algorithms for Worst-Case Design and Applications to Risk Management *
  • Contents vii
  • Preface xiii
  • Chapter 1 - Introduction to Minimax 1
  • References 17
  • Comments and Notes *
  • Chapter 2 - A Survey of Continuous Minimax Algorithms 23
  • References *
  • Comments and Notes *
  • Chapter 3 - Algorithms for Computing Saddle Points 37
  • References *
  • Comments and Notes *
  • Chapter 4 - A Quasi-Newton Algorithm for Continuous Minimax 63
  • References *
  • Appendix A - Implementation Issues *
  • Appendix B - Motivation for the Search Direction D̄ *
  • Comments and Notes *
  • Chapter 5 - Numerical Experiments with Continuous Minimax Algorithms 93
  • References 119
  • Chapter 6 - Minimax as a Robust Strategy for Discrete Rival Scenarios 121
  • References *
  • Chapter 7 - Discrete Minimax Algorithm for Equality and Inequality Constrained Models 139
  • References *
  • Chapter 8 - A Continuous Minimax Strategy for Options Hedging 179
  • References *
  • Appendix A - Weighting Hedge Recommendations, Variant B* *
  • Appendix B - Numerical Examples 237
  • Comments and Notes 244
  • Chapter 9 - Minimax and Asset Allocation Problems 247
  • References *
  • Comments and Notes *
  • Chapter 10 - Asset/liability Management under Uncertainty 291
  • References *
  • Comments and Notes *
  • Chapter 11 - Robust Currency Management 341
  • References *
  • Appendix - Currency Forecasting *
  • Comments and Notes *
  • Index 381
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